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Collision geometry and particle production in high energy heavy ion collision experiments


Chinese Physics C (HEP & NP)

Vol. 32, No. 4, Apr., 2008

Collision geometry and particle production in high energy heavy ion collision experiments *
WANG Ya-Ping( )
1)

ZHOU Dai-Mei(

)

2)

HUANG Rui-Dian(

) CAI Xu(

)

3)

(Institute of Particle Physics, Central China Normal University, Wuhan 430079, China)

Abstract An overview of research status of soft physics in high energy heavy-ion collision experiments and recent experimental results are presented. This paper includes four parts: 1) Theoretical predictions of quarkgluon plasma and introduction for high energy heavy ion collision experiments. 2) Experimental status on collision geometry. 3) Experimental status on particle production. 4) Conclusion and outlook for research status of soft physics in LHC/ALICE.

Key words quark-gluon plasma (QGP), soft physics, collision geometry, particle production PACS 25.75.-q

1

Introduction

The 19th International Conference on UltraRelativistic Nucleus-Nucleus Collisions (QM2006) was held in Shanghai, China on November 14—20, 2006. In the conference, relativistic heavy ion collider (RHIC) experiments (including BRAHMS, PHENIX, PHOBOS and STAR collaborations) at Brookhaven National Laboratory (BNL) gave many further surprising results from experimental data, and large hadron collider (LHC) experiments (including ALICE, ATLAS, CMS and LHCb collaborations) at European Organization for Nuclear Research (CERN) reported the progress & status of LHC and gave many prospective physics results of searching for QuarkGluon Plasma (QGP). Also, the Super Proton Synchrotron (SPS) experiments at CERN and the Institute for Heavy Ion Research (GSI) collaborations presented their results and new plan. More than 700 theorists and experimentalists participated in the exciting conference. In April 2005, the four experimental collaborations at RHIC announced jointly[1—4] that the RHIC had discovered a “perfect liquid” in high energy Au+Au collisions. The new state of nuclear matter behaviors like a liquid, not like a gas of free

quarks and gluons. This matter interacts much more strongly than originally expected, thus theorists gives it a new name “sQGP” (strongly interacting QGP). Dr. T. D. Lee said, “The discovery of the strongly interacting quark-gluon plasma is a historical event.” 1.1 Theoretical prediction phase transition between QCD and QGP states

The goal of the experimental heavy ion program at ultra-relativistic energies is to study Quantum Chromo-Dynamics (QCD) in an environment very di?erent from that encountered in hard processes, in a dense system of quarks and gluons[5] . The lattice calculations of QCD predict that nuclear matter undergoes a phase transition from hadron state to a decon?ned state of QGP at a critical temperature Tc , corresponding to an energy density of εc . The dissolution of massive hadrons into almost massless quarks and gluons at Tc leads to a very rapid rise of the energy density near the decon?nement transition, as shown[6] in Fig. 1. In Fig. 1, the curves labeled “2 ?avours” and “3 ?avours” were calculated for two and three light quark ?avours of mass mq /T =0.4, respectively. “2+1 ?avours” indicates a calculation for two light and one heavier strange quark ?avours of mq /T =1[8] . In this

Received 21 May 2007 * Supported by Ministry of Education of China (306022) and National Natural Science Foundation of China (10635020) 1) E-mail: wangyp@iopp.ccnu.edu.cn 2) E-mail: zhoudm@phy.ccnu.edu.cn 3) E-mail: xcai@mail.ccnu.edu.cn

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case the ratio ε/T 4 interpolates between two light ?avours at T Tc and three light ?avours at T 2Tc. For 2 and 2+1 ?avours the critical temperature is Tc =173±15 MeV[7] . The arrows on the right-side ordinates show the value of the Stefan-Boltzmann limit for an ideal quark-gluon gas.

spectrum thus will essentially be given by massless 2?avour QCD close to Tc and will rapidly switch over to the thermodynamics of massless 3-?avor QCD in the QGP phase. 1.2 Heavy-ion collision experiments at high energies

Fig. 1. Energy density in units of T 4 for QCD with two and three dynamical quark [7] ?avours .

A contribution to ε/T 4 , which is directly proportional to the quark masses and thus vanishes in the massless limit, has been ignored in these curves. Since the strange quarks have a mass ms ≈ Tc they will not contribute the thermodynamics close to Tc but will do so at higher temperatures[6] . Bulk thermodynamic observable of QCD with a realistic quark-mass

Searching for new physics in heavy ion collisions requires a detailed understanding of elementary nucleon-nucleon collision. As hydrodynamical theory, we can divide typically the collision process into three basic stages: initial conditions, hydrodynamic evolution (hard interactions and quark-gluon plasma) and freeze-out. After collisions, medium of high energy density and high temperature is created, with very high particle yields. Thus, it’s signi?cant that what we can see from “ashes” of the medium. The left panel of Fig. 2 shows inclusive charged particle transverse momentum (pT ) spectra obtained from p-p collisions at the Intersecting Storage Rings (ISR)[9] , and from p-? collisions by UA1[10] at CERN, p and by the Collider Detector at Fermilab (CDF)[11] at Fermi National Accelerator Laboratory (FNAL). With beam energy increasing high pT particle production is enhanced which re?ects the increase of the jet production cross-section.

Fig. 2. (a) Inclusive charged particle production for p-p and p-? collisions p soft particle production.

[9—11]

. (b) Schematic drawing of

In hadron-hadron reactions, hard scattering followed by fragmentation is considered to be the dominant process of hadron production for particles with pT >2 GeV/c at mid-rapidity. At low transverse momentum, where particles have pT <2 GeV/c, particle interactions are often referred to as “soft”[4] . The right panel of Fig. 2 shows the soft particles production spectrum. As it shows, the soft particles, with

small momentum transferred and pT <2 GeV/c, take more than 99% of the total particle yields. 1.3 Framework of the paper

This series of review are interested in research status of soft physics in high energy heavy ion collision experiments. As the ?rst part of the review, this paper will give an overview of global properties of soft

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physics, including collision geometry and particle production. This paper gives detailed description for these parts in Section 2 and 3, respectively. At last, the paper will give a conclusion for the status and an outlook for LHC experiments on soft physics. The following parts of the review will concentrate on the properties of hadronization, thermodynamics, correlations and ?uctuation presented by Prof. D. M. Zhou, Y. P. Wang et al[12] . We suggest the readers refer to an overview entitled “Experimental Status of Ultra-High Energy Induced Nuclear Reactions” presented by X. Cai[13] .

2

Collision geometry

The collision geometry (i.e. the impact parameter b) determines the number of participating nucleons Npart , and many observables in experiments are scaled with Npart , such as transverse energy, particle multiplicity, particle spectra and so on. The mean number of participating nucleons ( Npart ) can be estimated by (A-Nspec ) , and the number of spectators Nspec is measured by Zero-Degree Calorimeter (ZDC) apparatus. The mean number of binary nucleon-nucleon collisions ( Ncoll ) can be estimated using Monte-Carlo methods. we know that the smaller b, the more participants Npart , then the bigger collision system will be produced with higher particle yields. 2.1 Hydrodynamics description of high energy collisions

tions of relativistic hydrodynamics[15, 16] . It turns out that the strong compression along one axis leads to highly anisotropic distributions, with the Gaussian rapidity distributions of width σ = ln s/m2 . It is the application of the Fermi-Landau initial conditions to the generally-accepted formalism of 3D relativistic hydrodynamics that is the known as the “Landau hydrodynamics model”. The existing data are broadly well consistent with Landau’s original predictions from the 1950’s, as shown[14] in Fig. 3. However, the Landau model starts with a static initial state and rapidly generates the rapidity distribution by means of hydrodynamics. So, dNch /dη is not a static “initial-state” e?ect, but rather the result of a dynamical process in the very ?rst stages of the collision.

One of the major surprises from the RHIC data[1—4] has been the relevance of relativistic hydrodynamics in the overall understanding of the experimental data. The relevant geometry in the early stages of a heavy-ion collision or a p-p collision is one characterized by the nuclear radius in the transverse direction, and a large contraction in the longitudinal direction. We already see the relevant time scales for longitudinal and transverse dynamics are very di?erent, of order τT ≈ R/c, (approximately several fm/c) √ in the transverse direction and τL ≈ mR/(cs s)( 1 fm/c) in the longitudinal direction[14] . 2.1.1 Landau hydrodynamics model Fermi and Landau considered a system with the geometry just described above, replacing the potential complexities of a high energy nuclear collision √ with a slab of area πR2 and length ? = mR/ s (and √ thus volume V ∝ R3 / sNN ) in which all of the energy of the incoming projectiles is assumed to thermalize. In a nuclear collision, the total entropy in the collision volume is S, S ∝ V ∝ Npart , leading to the Npart -scaling of total multiplicities. This statistical model was extended by Landau with using the equa-

Fig. 3. (A) Nch compared for A-A, e+ -e? and [17, 18] p-p collisions . (B) BRAHMS data dN /dy for charged pions at 200 GeV, ?t to a Gaussian. The inset shows the width divided by the Landau expectation as a function of √ [19] sNN .

2.1.2 Bjorken hydrodynamics model Landau hydrodynamics seems to be relevant to the physics in the very early stages (τ 1 fm/c). By contrast, hydrodynamic calculations which assume boost-invariance in the initial conditions have been used for quantitative comparisons with experimental observables that are sensitive to early-time pressure gradients[20] . These models are presented by Bjorken[21] , who postulated the imposition of boost-

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invariance[22] as a guiding principle for high energy interactions. Since the calculations are initialized at time scales on the order of 1 fm/c, they are unable to calculate the initial-state entropy. However, given this single piece of experimental data, and an assumed equation of state (usually a hybrid of the Landau EOS and a hadronic EOS, with a mixed phase), they are able to successfully calculate the effects of transverse pressure on particle spectra (radial ?ow) the mapping from the initial-state geometry to anisotropies in the ?nal-state transverse momentum distributions (elliptic ?ow)[20] . Several clear signatures of radial ?ow are present in the experimental data even without recourse to particular models[14] . At low transverse momentum (pT < m) it is observed that the particle spectra harden with increasing particle mass. Elliptic ?ow has now been comprehensively described by calculations using boost-invariant hydrodynamics, both as a function of centrality and pT . A instance is shown in left panel of Fig. 4, which exhibits that the asymmetry parameter v2 has a dependence of transverse momentum. Given the obvious discrepancy between the assumption of boost-invariance used in these calculations and the manifestly boost non-invariant particle distributions shown by the BRAHMS[1] data, it is not surprising to ?nd that it is di?cult to reproduce the dependence of v2 on η as measured by PHOBOS[2] ,

as shown[23] in the right panel of Fig. 4. It shows that we need to understand the initial conditions in some detail. In conclusion, we have found that the hydrodynamics approach is well consistent with a wide range of data, although no existing model or code can describe every detail correctly. This is especially true when considering longitudinal dynamics, which has not yet been fully incorporated into models that describe many features of the transverse dynamics[14] . 2.2 Centrality

As mentioned above, we characterize centrality by number of participants Npart (?volume) or number of binary collisions Ncoll . Once the choice of pseudorapidity region for the centrality determination is made and the corresponding e?ciency is determined, the resulting multiplicity related distribution can be divided into percentile of total cross-section bins. Comprehensive MC simulations of these signals, that include Glauber model calculations of the collision geometry, allow the estimation of Npart for a cross section bin. Shown[24] in the left panel of Fig. 5 is the ratio ν, which is the average number of binary nucleonnucleon collisions every nucleon undergoes within a nucleus-nucleus collision, as a function of the Npart . As this plot shows, a study of the centrality dependence of particle production allows a large variation of ν. The right panel in Fig. 5 shows[25] the measured dNch /dη distributions for charged particles for several di?erent centrality ranges. A similar parameter, typically denoted with ν and ? calculated from ν =(Aσpp )/σpA where the σ’s are in? elastic cross sections, is commonly used to characterize centrality or target dependence of observables in p-A collisions[26] . In nucleus-nucleus collisions, the calculated average number of collisions per participant varies by a large factor as a function of centrality and also has some dependence on energy due to the varying nucleon-nucleon cross section[2] . Centrality is typically parameterized by the number of participating nucleon pairs (Npart /2), or the number of binary nucleon-nucleon collisions (Ncoll ), in the overlapping region. Both quantities grow with the increasing centrality (decreasing impact parameter) of the collision. 2.3 Energy density

Fig. 4. (a) v2 as a function of pT for various particle species, compared to a hydrodynamicsinspired ?t. (b) v2 as a function of η compared with 3D hydro calculations.

In ultra-relativistic heavy ion collisions, the maximum energy density occurs just as the two highly Lorentz contracted nuclei collide. In any reference frame, the more interesting quantity is the energy density carried by particles which are closer to equilibrium conditions. These conditions are roughly equivalent to restricting the particles to a range of

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Fig. 5. (a) Ratio ν vs. Npart for inelastic process for RHIC, SPS and low alternating gradient synchrotron (AGS) experiments from PHOBOS Glauber MC. (b) Distributions of dNch /dη for centrality ranges of, top to bottom, 0%—5%, 5%—10%, 10%—20%, 20%—30%, 30%—40%, and 40%—50% in Au+Au collisions at √ sNN = 200 GeV.

pseudorapidity |η| <1. Because there are no means to directly measure energy density, it must be inferred from the properties of the detected particles. PHOBOS data[2] have been used to investigate what range of initial energy densities is consistent with the observations. Studies of pseudorapidity and transverse momentum distributions, as well as elliptic ?ow, have been combined to constrain assumptions about the energy in the system and the time evolution of the volume from which the particles emanate. As shown in Fig. 20, the produced particle densities are at their maximum near midrapidity and increase with both collision energy and centrality. It is notable that multiplicity measurements were initially obtained by PHOBOS and later con?rmed by the other experiments at every new beam energy and species provided during the ?rst three RHIC runs[2] . The right panel of Fig. 24 is a compilation of the evolution of the midrapidity charged particle density, dNch /dη|η|<1 , per participating nucleon pair, Npart /2 , as a function of collision energy. Before attempting to make detailed estimates of the energy density, it is important to stress that the midrapidity particle density at the top RHIC energy is about a factor of two higher than the maximum value seen at the SPS[27] and there is evidence that the transverse energy per particle has not decreased[28, 29] . Thus, with little or no model dependence, it can be inferred that the energy density has √ increased by at least a factor of two from sNN =17 to 200 GeV. In addition to the measured particle multiplicities, we must know the average energy per particle carried in order to estimate the energy density more precisely, as well as the volume from which they originate. PHOBOS data for the transverse momentum distribution of charged particles[30] can be used to ?nd a mean transverse momentum. Fig. 6

compares the identi?ed particle yields at very low transverse momentum measured by PHOBOS[31] and PHENIX data[32] for higher momenta.

Fig. 6. Transverse momentum distributions of identi?ed charged particles emitted near midrapidity in central Au+Au collisions at √ sNN = 200 GeV.

The low momentum identi?ed particle data shown in Fig. 6 are in non-overlapping regions of pT for the three di?erent species. Accounting for the yields of the various particles, an average transverse momentum for all charged particles of pT ≈500 MeV/c can be derived. Averaging over the pions, kaons, and nucleons, and assuming the yields for the unobserved neutral particles, an average transverse mass, mT , of ≈570 MeV/c2 can be extracted. The total energy in the system created near √ midrapidity in central Au+Au collisions at sNN = 200 GeV can be found from[2] Etot = 2Epart dNch /dη|η| 1 fneut f4π . (1)

where Epart is the average energy per particle,

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dNch /dη|η| 1 =655±35 (system) is the midrapidity charged particle density for the 6% most central collisions, fneut is a factor of 1.6 to roughly account for the undetected neutral particles, and the factor of 2 integrates over ?1 η 1. The correction for these additional particles, f4π , is trivially estimated from the fraction of solid angle outside θ=40?—140? . (i.e., outside |η| 1) and equals about 1.3. It should be stressed that this methodology does not suggest that the entire distribution of particles is isotropic. Instead, the goal is to obtain the energy density for the component of the distribution which is consistent with the isotropic emission from a source at midrapidity. Combining all of these terms, the total energy contained in all particles emitted near midrapidity, with transverse and longitudinal momenta consistent with emission from an equilibrated source, is about 1600 GeV. The next thing we should know is the volume within which this energy is contained at the earliest time of approximate equilibration. For central collisions, a transverse area equal to that of the Au nuclei (≈150 fm2 ) can be assumed, but which value to use for the longitudinal extent is not as clear. One extreme[2] is to take the very ?rst instant when the two Lorentz contracted nuclei overlap (longitudinal size ≈0.1 fm), which yields an upper limit on the energy density in excess of 100 GeV/fm3 . There is, however, no reason to assume that at such an early instant the system is in any way close to equilibrium. A second commonly-used assumption is that proposed by Bjorken[21] , namely, a transverse size equal to the colliding nuclei and a longitudinal size of 2 fm (corresponding to a time of the order of τ ≈1 fm/c since the collision) which implies an energy density of about 5 GeV/fm3 . This estimate is much higher than the energy density inside nucleons. 2.4 Degree of nuclear stopping

Fig. 7. The projectile component of the net proton distribution in elementary and nuclear interactions for two centralities.

Baryon stopping for central collisions at ultrarelativistic energies increases with system size. The integrated yield and rapidity density of negative hadrons exhibit scaling with the number of participant nucleons for nuclear collisions, and a small enhancement with respect to A+A collisions[35] , as shown in Fig. 8.

Through baryon stopping mechanism we can get that it de?nes available energy for particle production. The independence of the forward and backward hemispheres (hadronic factorization) suggests a picture of hadronic interactions where the net baryon distribution is built up from two components: one connected to the target and the other to the projectile[33] . In Fig. 7 this projectile component is presented[34] . With increasing centrality, the projectile component of the net proton distribution has a similar behavior in p-A and A+A interactions, demonstrated in Fig. 7, exhibiting a smooth transition of baryon number transfer from the elementary to the more complex nuclear interactions. But for p-p interactions the xF distribution is ?at and has about 50% energy loss.

Fig. 8. Upper: The normalized rapidity distributions of p-? for Pb+Pb collisions. Also p ? shown are the corresponding Λ-Λ rapidity distributions, and the scaled proton distribution for p-p collisions. Lower: The normalized rapidity distributions of NB ? NB from ? Equation NB ?NB = (2.07±0.05)?(Np ?Np )+ ? ? (1.6±0.1)?(NΛ ? NΛ ) for Pb+Pb, and scaled ? NB ? NB for S+S. ?

Baryon number is conserved, and rapidity distributions are only slightly a?ected by rescattering in late stages of the collision, the measured net-baryon ? (B ? B) distribution retains information about the energy loss and allows the degree of nuclear stopping to be determined[36] . Such measurements can also distinguish between di?erent proposed phenomenological mechanisms of initial coherent multiple interactions and baryon transport[37—39] . Bjorken assumed

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that su?ciently high energy collisions are “transparent”, thus the midrapidity region is approximately net-baryon free[21] . Figure 9 shows net-proton dN /dy measured at AGS and SPS compared with these results[36] . The net-proton distribution shows that collisions at RHIC energies are quite transparent compared with lower energies.

the target (or projectile) rest frame. The η =η?ybeam variable is used. It is measurable without particle identi?cation and approximately transforms the distributions to the rest frame of one of the colliding particles/ions. The rapidity, y, is de?ned as E + pz . Rapidity variables are in the centery = 0.5 ln E ? pz of-mass system with yp positive. The pseudorapidity variable η is related to the particle emission angle θ with η = ? ln[tan θ/2]. In proton-proton collisions, the so-called limiting fragmentation[40] is seen from a few GeV to 900 GeV collision energy (e.g. at CDF, UA5 and ISR). The left panel of Fig. 11[41] shows that the charged particle pseudorapidity density distributions are approximately independent of collision energy over a large √ range of η , which grows with s. The same phenomenon is observed in e+ -e? collisions, as shown in the right panel of Fig. 11[42] .

Fig. 9. The net-proton rapidity distribution at √ [35] AGS (Au+Au at sNN = 5 GeV), SPS √ (Pb+Pb at sNN = 17 GeV) and this mea√ surement ( sNN = 200 GeV).

Figure 10 the inserted plot shows the extrapolated net-baryon distribution (data points) with ?ts (represented by the curves) to the data[36] . The full ?gure shows the rapidity loss as a function of projectile rapidity (in the Center-of-Mass). By extrapolation to the full net-baryon distribution, we ?nd that the rapidity loss scaling observed at lower energy is broken and the rapidity loss seems to saturate between SPS and RHIC energies.

Fig. 10. (insert) The net-baryon dN /dy obtained from the measured net-proton dN /dy. (Full) The rapidity loss. Fig. 11. (a) Pseudorapidity density distributions of charged particles emitted in p(?)-p p [43—45] collisions at various energies . (b) Similar data for particles emitted along the jet axis in an e+ -e? collision versus the variable [46] yT -yjet .

2.5

Limiting fragmentation

In order to understand the relation between particle production and collision mechanisms, we consider particle production away from mid-rapidity in

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As Fig. 12 showed[41] , similar scaling was observed √ for p-A collisions between sNN =6.7 and 38.7 GeV, √ and more recently in d-Au collisions at sNN = [47, 48] 200 GeV . The observed energy-independence of these distributions holds both for the projectile and for the target reference frames[47] .

Fig. 14. The ratio of dNch /dη per participant pair between central (0%—6%) and noncen√ tral (35%—40%) data plotted for sNN =200, 130, and 19.6 GeV.

Fig. 12. Pseudorapidity density distributions of charged particles emitted in d-Au, p-emulsion collisions at various energies.

First, limiting fragmentation (energy independence of dN/dη ) is valid over a large range of η . Second, the scaled dN /dη shape is not independent of centrality at high η. The η distribution is broader in peripheral collisions than in central collisions. Third, as in p-? collisions, the fragmentation p region in Au+Au collisions grows in pseudorapidity extent with beam energy, which is becoming a dominant feature of the pseudorapidity distributions at high energy. 2.6 Leading particle e?ect

The data from PHOBOS show a number of interesting features, as shown in Fig. 13 and Fig. 14[49] .

Fig. 13. The distribution dNch /dη per participant pair for central (0%—6%) and noncentral √ (35%—40%) Au+Au collisions for (a) sNN = √ 200 GeV and (b) sNN = 19.6 GeV.

In hadron-hadron and lepton-hadron interactions, a well-known feature is that one particular particle in the ?nal state often has a momentum close to the maximum permitted. This observation is commonly referred to as the “leading particle e?ect”, and it has been related to the quantum number ?ow from the initial state to the particle in the ?nal state, on the basis that the particle which carries more constituents of the initial state will have a sizable fraction of the four-momentum of the initial state[50] . The PHOBOS experiment has demonstrated two kinds of universal behavior are observed in charged particle production in heavy ion collisions at three RHIC energies[51] . One is that forward particle production follows a universal limiting curve with a nontrivial centrality dependence over a range of energies. The other arises from comparisons with pp/?p and p + ? e e data, Nch / Npart /2 in nuclear collisions at √ high energy scales with s in a similar way as Nch in e+ e? collisions and has a very weak centrality dependence. As shown of Fig. 15(a), the comparisons can be seen more clearly by dividing all of the data by a ?t to the e+ e? data, seen in Fig. 15(b). The pp/?p p data follows the same trend as e+ e? , but it can be shown that it matches very well if the “e?ective en√ √ ergy” se? = s/2 is used, which accounts for the leading particle e?ect seen in pp collisions[52, 53] .

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sions su?ered per participant. In this situation, the Au+Au data suggest a reduced leading particle e?ect in central collisions of heavy ion at high energy. The yield of high transverse momentum (pT 5 GeV/c) leading particle in Au+Au collisions at the top RHIC √ energy, sNN = 200 GeV, is suppressed by a factor of about ?ve lower than expected from the measurements in p-p collisions at the same energy[54, 55] . The absence of this e?ect in d-Au collisions at the same energy supports the partonic energy loss scenario[56] . The leading-particle suppression is usually quanti?ed by the nuclear modi?cation factor, d2 NAA /dpT dη . Ncoll centrality class d2 Npp /dpT dη (2) as the ratio of the yield in A+A over the binaryscaled yield in pp for a given centrality class. √ At mid-rapidity, in Au+Au collisions at sNN = 200 GeV, RAA is found to decrease from the peripheral (RAA 1) to the central events (RAA 0.2), for pT 5 GeV/c (see Fig. 16). RAA (pT , η) = 1 ×

Fig. 15. Comparison of Nch / Npart /2 for A+A, pp/?p (a) and e+ e? data compared p with a ?t to the e+ e? data (b).

This feature may be related to a reduction in the leading particle e?ect due to the multiple colli-

Fig. 16.

RAA (pT ) in Au+Au collisions at

√ sNN = 200 GeV for di?erent centralities.

3
3.1

Particle production
Rapidity distribution

longitudinal phase space, and consider the pseudorapidity equal to the rapidity approximately. We can describe the relations between the rapidity and the pseudorapidity by Eq. (3). dN dN =β . dηdpT dydpT (3)

As the de?nitions for rapidity y and pseudorapidity η, we use rapidity distribution to describe the

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where the parameter β indicates a discrepancy between η and y. We generally set β to 1.1 in calculations. Pseudo-rapidity distributions in p-p collisions are shown[57] in Fig. 17. The pseudorapidity distributions of charged particles with HIJING model are in good agreement with the energy dependence of the collider data[43, 58] .

found to agree well with the participant scaling in terms of the respective fragments away from midrapidity, seen in Fig. 18. Overall, model calculations based on both soft physics and perturbative QCD (HIJING, AMPT) lead to excellent agreement with the experimental results. Calculations based on the saturation picture using scale parameters set by previous experimental data fail to reproduce the measurements and lead to a pseudorapidity dependence very di?erent from that observed with the current data[48] . Pseudorapidity distributions in d-Au collisions are shown in Fig. 18[48] and Fig. 19[47] , respectively.

Fig. 17. Pseudorapidity distributions of charged particles in non-single-di?ractive pp at √ √ sNN = 53 GeV, p-? collisions at sNN = p 200, 540, 900 and 1800 GeV.

Pseudorapidity densities of charged particles for √ the d-Au reaction at sNN = 200 GeV are presented for di?erent centrality ranges. The ratio of particle densities for the central and the peripheral events is

Fig. 18. (a),(b) Charged-particle pseudorapidity densities for indicated centrality ranges. (c) Multiplicity ratios R0—30 (squares) and R30—60 (triangles).

√ Fig. 19. Comparison of dNch /dη distributions for d+Au collisions at sNN = 200 GeV to p+Em collisions (sum of shower and gray tracks) at ?ve energies with η shifted to η ? ybeam (a) and η + ytarget (b).

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Fig. 20. dNch /dη vs η (solid and open points) for ?ve centrality bins representing 45% of the total cross √ √ section for sNN = 19.6 GeV Au+Au collisions and for six centrality bins for sNN =130 and 200 GeV [49] corresponding to 55% of the cross section .

In Fig. 19, the η measured in the center-of-mass system has been shifted to η?ybeam in order to study the fragmentation regions in the deuteron/proton rest frame. Similar to this, but η ha been shifted to η+ytarget in order to study the fragmentation regions in the gold/emulsion rest frame. From all above, we can ?nd the longitudinal features of d-Au collisions at √ sNN = 200 GeV, as re?ected by the centrality dependence of the pseudorapidity distributions of charged particles, are very similar to those seen in p-A collisions at energies lower by more than an order of magnitude. Pseudorapidity distributions in Au+Au collisions are shown in Fig. 20[49] . From the ?gure, we can ?nd that for central collisions at the highest energy, we ?nd that a total of more than 5000 charged particles are produced. These results span 11 units of pseudorapidity, a factor of 10 in energy, and a factor of 5 in Npart -all measured in a single detector. While the scaled multiplicities increase with centrality at midrapidity, Fig. 21[25] shows they are independent of both the collision centrality and the beam energy over a pseudorapidity range from 0.5 to 1.5 units below the beam rapidity. This is found for energies ranging from the √ CERN/SPS energy ( sNN = 17 GeV)[59] to the present RHIC beam energy and is consistent with a limiting-fragmentation picture in which the excitations of the fragment baryons saturate at a moderate collision energy, independent of system size[60] . The increased projectile kinetic energy is utilized for particle production below beam rapidity, as evidenced

by the observed increase in the scaled multiplicity for central events at midrapidity.

Fig. 21. Charged-particle multiplicities normal[59] ized to the Npart pairs for the Pb+Pb data [60] and the Au+Au results .

3.2

Angular distribution

Some of the general properties of charged particle multiplicity distributions[61] may be seen in Fig. 22. Panel a: The pseudorapidity density, dN/dη is shown as a function of η. Panel b: The corresponding angular distribution dN/dθ is shown as a function of the angle θ relative to the beam axis. Panel c: the same as for panel (b) but here dN/d? is shown. The shaded regions in panels (a) and (b) indicate the angular region where the transverse momentum pT exceeds the longitudinal momentum p|| . Since the particles emitted within the angular region 45? < θ < 135? corresponding to ?0.88 < η < 0.88 (grey bands in panels (a) and (b)) are most likely to represent a thermalized region of phase space, there is a special signi?cance attached to the number of

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charged particles emitted in this region, i.e. the height of the mid-rapidity plateau or dNch (|η| < 1)/ dη. Although this region appears as a plateau in the dNch /dη-distribution shown in Panel (a) it is interesting to observe that the dNch /dθ and the dNch /d?

distributions both exhibit a minimum at θ=90? corresponding to η=0. As shown in Fig. 22, there are only 22% of the total emitted charged particles with pT > p|| , however, these particles carry information about the densest region form in the collisions.

Fig. 22.

Illustration charged particle distribution for 0%—6% central 200 GeV Au+Au collisions.

3.3

Multiplicity distribution

In Fig. 23 we show the normalized yield per participant obtained for Au+Au collisions, protonantiproton (p-?) collisions[43] and central Pb+Pb colp lisions at the CERN/SPS.

Fig. 23. Measured pseudorapidity density normalized per participant pair for central [43, 62] Au+Au collisions .

Several important features of the data emerge: First, the central Au+Au collisions show a signi?cantly larger charged particle density per participant than for example non-single di?ractive (NSD) p-? colp lisions at comparable energies. This rules out simple superposition models such as the wounded nucleon model[63] and is compatible with the predictions of models like HIJING that include particle production via hard-scattering processes. Secondly, the observed increase by 31% from 56 to 130 AGeV in central Au+Au collisions is signi?cantly steeper than the increase shown by a p-? parametrization p

(see Fig. 23) for the same energy interval[43] . Finally, comparing the RHIC data with those obtained √ at the CERN/SPS for Pb+Pb collisions at s = 17.8 AGeV, we ?nd a 70% higher particle density per par√ ticipant near η=0 at s=130 AGeV. General arguments suggest that this increase should correspond to a similar increase in the maximal energy density achieved in the collision. Several theoretical predictions had been made concerning the density of charged particles at mid√ rapidity for sNN = 200 GeV central Au+Au collisions, shown in the left panel of Fig. 24[2] . It is evident that most of the predictions overestimated the density by up to a factor of two although a few predictions agree with the measurements. Among the models which predicted a value close to that seen in the data were two which invoked the concept of saturation in either the initial state or the produced partons. However, the search for other evidence for possible parton saturation e?ects remains a topic of interest at RHIC. The dependence on collision energy is shown in the right panel of Fig. 24[2] . The PHENIX results for Nch are compared with the data available from the other RHIC experiments[65] . This comparison is shown in the left panels of Fig. 25. There is good agreement between the results of BRAHMS[25, 60] , PHENIX, PHOBOS[62, 66, 67] , and STAR[68, 69] using Npart based on a Monte CarloGlauber model. This agreement is very impressive because all four experiments use di?erent apparatuses

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and techniques to measure the charged particle production. The systematic errors of all results are uncorrelated, except for those related to the same Glauber model, which are small. That makes it pos-

sible to calculate the RHIC average and reduce the systematic uncertainty. The averaged results from all four RHIC experiments are plotted in the right panel of Fig. 25.

Fig. 24. (a) A compilation of theoretical model predictions (solid squares) of the midrapidity density of charged [64] particles dNch /dη or dNch /dy . (b) The energy dependence of the pseudorapidity density at |η| < 1.

Fig. 25. (a) dNch /dη per pair of Npart measured by the four RHIC experiments at di?erent energies. (b) RHIC average values (including PHENIX) compared to the PHENIX results.

It should be pointed out that the universal Npart scaling of the total number of particles produced in Au+Au collisions does not result from rapidity distributions whose shape is independent of centrality, or Npart . The rapidity distributions do depend on both centrality and on the nature of the colliding systems, as is evident from Fig. 26[2] for Au+Au collisions[49] . The data have been divided by the average number of pairs of participating nucleons for each energy and

centrality range. Comparison of the total charged-particle multiplicity in RHIC with e+ e? and pp/p? data is shown p as Fig. 27[17] . Figure 27(a) shows the shapes of Au+Au and e+ e? are similar (within 10%) in shape and magnitude, especially within |η| <4. It is observed that the Au+Au data are very similar in magnitude and √ shape to the e+ e? data at the same s, and similar

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in shape to the pp data (as shown in Fig. 27(b)), over a large range in η. The di?erences between the e+ e? and Au+Au distributions shown in Fig. 27(a) can be partly attributed to the di?erent kinematic variables.

of η ? ybeam is independent of centrality. Energy independent LF behavior for charged particles can be seen in Fig. 29(b). It also indicates that there is apparently an important charged baryon contribution in nucleus-nucleus collisions at the forward η region.

Fig. 26. Distributions of normalized pseudorapidity densities of charged particles emitted in Au+Au collisions at two energies and two ranges of centrality.

Fig. 28. Variation of Nγ per participant pair in 2.3 η 3.7 versus Npart . The lower band re?ects uncertainties in Npart calculations.

Fig. 27. (a) dNch /dη/ Npart /2 for central Au+ √ Au collisions at sNN = 200 GeV compared + ? with pp and e e data. (b) Au+Au and p-p data divided by a ?t to the Au+Au data.

Multiplicity and pseudorapidity distributions of √ photons in Au+Au collisions at sNN = 62.4 GeV[70] is shown as Fig. 28 and Fig. 29. Fig. 28 shows the Nγ per Npart pair is approximately constant with centrality. Approximate linear scaling of Nγ with Npart in the η range studied indicates that photon production is consistent with the nucleus-nucleus collisions being a superposition of nucleon-nucleon collisions. We observe in Fig. 29(a) that photon results from the SPS and RHIC are consistent with each other, suggesting that photon production follows an energy independent LF (Limiting Fragmentation) behavior, and also observe that dNγ /dη as a function

Fig. 29. (a) Variation of dNγ /dη normalized to Npart with η ? ybeam for di?erent collision energy and centrality. (b) same as (a) for charged particles.

At midrapidity the charged particle multiplicities have been measured for Au+Au collisions as a function of both energy and centrality of the collisions. A surprising result is that the dependence on these two variables can be factorized to high accuracy (? 1%)[71] , as shown in Fig. 30. 3.4 Scaling behavior

Scaling of charged particle production in d-Au col√ lisions at sNN = 200 GeV[47] is shown in Fig. 31 and

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the total number of participants, that the transition between the multiplicity per participant in d-Au and Au+Au collisions is not controlled simply by the total number of participants, and that the energy dependence of the density of charged particles produced in the fragmentation regions exhibits extensive longitudinal scaling.

Fig. 30. (a) The pseudorapidity density, dN/dη at |η| <1 is shown as a function of Npart for Au+Au and pp/p? collisions. (b) The ratio of p the data to the ?t function f (s) × g(Npart ) is seen to lie in a narrow band around unity. Fig. 32. Centrality dependence of the dNch /dη ratio of d-Au collisions relative to that for in[58] elastic p(? )-p collisions p at the same energy.

Fig. 31. Panel (a): Total integrated charged particle multiplicity per participant pair in [17] [72, 73] d-Au, Au+Au , p(? )-p inelastic p and √ [74] p(? )-p NSD p collisions at sNN = 200 GeV. pp Panel (b): The ratio RA = Nch /Nch , where pp Nch is the total number of charged particles for inelastic p(?)-p collisions, as a function of p Npart for di?erent collision systems.

PHOBOS has measured the charged particle pseudorapidity density at midrapidity (|η| <1) for Au+Au √ collisions at energies of sNN = 19.6 and 200 GeV[75] . As shown in Fig. 33, we ?nd an increase in particle production per participant pair for Au+Au collisions compared with the corresponding inelastic p(?)p p values for both energies. The ratio of the measured yields at 200 and 19.6 GeV shows a clear geometry scaling over the central 40% inelastic cross section and averages to R200/19.6 = 2.03±0.02(stat)±0.05(syst). In Cu+Cu and Au+Au collisions at the same collision energy, the charged hadron dN/dη distributions are nearly identical in broad pseudorapidity range with the same Npart , as shown in the left panel of Fig. 34[76] . Meanwhile, the increase in particle production per participant with increasing Npart is independent of collision energy over the full energy range of RHIC from 19.6 to 200 GeV, as shown in the right panel of Fig. 34[76] . 3.5 Transverse momentum distribution

Fig. 32. We ?nd that in d-Au collisions the total multiplicity of charged particles scales linearly with

Transverse momentum distributions are one of the most common tools used in studying high energy collisions. This is because the transverse motion is generated during the collision and hence is sensitive to the dynamics[8] . The yield of charged hadrons produced in collisions of gold nuclei at an energy of

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Fig. 33. (a) The measured pseudorapidity density per participant pair as a function of N part for Au+Au √ collisions at sNN = 19.6 GeV (closed squares), 200 GeV (closed circles). (b) The ratio, R200/19.6 , of the midrapidity pseudorapidity density per participant pair at 200 and 19.6 GeV versus N part .

Fig. 34. (a) Pseudorapidity distribution for charged hadrons in Cu+Cu (closed symbols) and Au+Au collisions √ (open symbols) at sNN = 200 GeV. (b) Ratio of mid-rapidity densities as a function of Npart .

sNN = 62.4 GeV has been measured with the PHOBOS detector at RHIC. The data are presented as a function of transverse momentum (pT ) and collision centrality. The goal of these measurements is to study the modi?cation of particle production in the presence of the produced medium by comparing with nucleon-nucleon collisions at the same energy[77] . In Fig. 35, PHOBOS presents the invariant yield of charged hadrons as a function of transverse momentum, obtained by averaging the yields of positive and negative hadrons. Data are shown for six centrality bins and are averaged over a pseudorapidity interval 0.2 < η < 1.4. Figure 36 shows the pT distributions for pions, kaons, protons, and antiprotons in both central (top panel) and peripheral collisions (bottom panel) in PHENIX experiment[32] . The pion spectra have a concave shape at low pT where many of the pions may come from the decay of resonances: ?, ρ, etc. The kaon spectra are approximately exponential over the



full measured pT range, whereas the proton spectra ?atten at low pT for the most central collisions.

Fig. 35. Invariant yields for charged hadrons √ from Au+Au collisions at sNN =62.4 GeV.

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Fig. 36. Transverse momentum distributions for pions, kaons, protons, and antiprotons in Au+Au collisions √ at sNN =200 GeV.

Fig. 37

pT of particles as a function of centrality (Npart ) in Au+Au collisions at

√ sNN = 200 GeV.

The average transverse momentum, pT , or the mean transverse kinetic energy, mT ? m0 , or the asymptotic slope are taken as measures of the temperature, T , of the reaction[78] . The pT of hadrons has a dependence of Npart , as shown in Fig. 37[32] . The PHENIX results incontrovertibly demonstrate that there is a strong and centrality dependent suppression of the production of high-pT pions relative to pQCD-motivated expectations. To better demonstrate the suppression, Fig. 38 shows

RAA (pT ) for mid-rapidity π0 ’s in central and peripheral 200 GeV Au+Au collisions[55] , and also in d-Au collisions[79] . Figure 38 shows that the central Au+Au π0 suppression changes only slightly over the measured pT range and reaches an approximately pT -independent factor of 5 (RAA ≈0.2) for pT >4—5 GeV/c. But we can not rule out a slight suppression by peripheral RAA . In all of the data sets RAA increases with increasing pT for pT < 2 GeV/c. Despite the di?erences

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resulting from the protons, the charged particles and π0 ’s exhibit very similar trends in the suppression vs. pT and vs. centrality. Meanwhile, no high pT jet suppression is observed for d-Au collisions, and the RAA > 1 for pT >4—5 GeV/c. To the further analysis for Fig. 38, we can get that the high-pT yields of both charged hadrons and π0 ’s per participant increase proportional to TAB for small Npart but level o? and then decrease with increasing Npart in more central collisions.

due to initial and ?nal state multiple scattering (the “Cronin e?ect”), the medium-induced energy loss of fast partons, and the e?ects of collective transverse velocity ?elds and of parton recombination[80] . The PHOBOS observations show that, surprisingly, the combination of all e?ects leads to a remarkably similar centrality evolution of the yields at high and low transverse momenta, providing a challenge to theoretical descriptions. That this is not accidental is suggested by the agreement with earlier mea√ surements at sNN = 130 GeV. The lower energy data[81, 82] , when compared over the same centrality range, show very similar centrality scaling, even though the yield at high pT increases much more rapidly with increasing beam energy than the overall particle yield. It has recently been argued that the observed scaling could be naturally explained in a model assuming the dominance of surface emission of high pT hadrons[83] . However, the approximate participant scaling has also been explained in the context of initial state saturation models[84] , as shown in Fig. 39 where
part RAA =

N

inel σpp d2 NAA /dpT dη Npart /2 d2 σpp /dpT dη

Fig. 38. π0 RAA (pT ) for central 0%—10% and peripheral 80%—92% Au+Au collisions and minimum-bias d-Au collisions.

and
part RPC =

N

Particle production at pT > 1 GeV/c in heavy-ion collisions is expected to be in?uenced by the interplay of many e?ects[77] . This includes pT broadening

0%—6% Npart d2 NAA /dpT dη . 0%—6% Npart d2 NAA /dpT dη

Data are shown in six bins of centrality, ranging from Npart =61 to 335 for 62.4 GeV collisions.

Fig. 39. Ratio of pT distributions from Au+Au collisions to various reference distributions at (?lled symbols) and 200 GeV (open symbols).

√ sNN =62.4 GeV

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Fig. 40.

Ratio of yields at

√ sNN = 200 GeV to 62.4 GeV for Cu+Cu (?lled circles) and Au+Au (open circles).

As shown in Fig. 40, the ratio of yields in 200 GeV to 62.4 GeV is plotted versus centrality for a range of transverse momenta[85] . It shows that the ratio of yields in Cu+Cu has only a moderate centrality dependence and is consistent with the Au+Au value for all measured pT . The observed suppression of high-pT particle production at RHIC is a unique phenomenon that has not been previously observed in any hadronic or heavy ion collisions at any energy. The suppression provides direct evidence that Au+Au collisions at RHIC have produced matter at extreme densities, greater than ten times the energy density of normal nuclear matter and the highest energy densities ever achieved in the laboratory[4] .

4

Conclusion and outlook

Ultra-relativistic heavy ion collisions probably produce a new form of matter[86, 87] . So the general concepts to nuclear matter is not suitable any more, and need to discover new principles or mechanism[88] . In J. Zim?nyi’s talk given at the a 18th International Conference on Ultra Relativistic Nucleus-Nucleus Collisions[89] , “Although theoretical models supported the early concept, the experimental data forced to change these speculations step by step.” After the overview of research status of soft physics in high energy heavy ion collision experiments, especially on basis of the recent experimental results, we try to give a conclusion as follows: 1) In central A+A collisions at RHIC energies, a high energy density medium is created. The energy density is estimated to be larger than 3 GeV/fm3 , which exceeds the critical energy density needed to form decon?ned phase predicted by lattice QCD. As mentioned above, the RHIC experiments have discovered a new form of nuclear matter, “sQGP”, which is

strongly interactive, but not weakly interacting QGP. 2) The hydro approaches (Bjorken hydrodynamical model and Laudau hydrodynamical model) behave very well over a wide range of data. In p-p collisions, leading particle e?ect exists, ?at distribution of xF is nearly independent of energy, and only about 50% of energy is available for particle production. But the leading particle e?ect is suppressed in A+A collisions in high pT range (not appeared in p-p collisions), and about 70%—80% of energy is available for particle production. Stopping e?ect in A+A collisions is comparable with expectations from p-A collisions. 3) Many of the experimental data can be expressed in terms of simple scaling behaviors. In particular, the data clearly demonstrate that proportionality to the number of participating nucleons, Npart . The total multiplicity and charged particle density per participant from di?erent systems are close to identical when compared at the same available energy, and many characteristics of the produced particles factorize to a surprising degree into separate dependence on centrality and beam energy. This feature of multiplicity in A+A, p-p and e+ e? collisions is possibly caused by parton saturation e?ect. The limiting fragmentation scaled by Npart is not independent of centrality at high pseudorapidity, and grows in pseudorapidity extent with beam energy. The experimental data from LHC, will help to further evaluate the range of validity of these scaling behaviors. In Dr. T.D. Lee’s overview[90] , “The strongly interactive quark-gluon plasma can be produced by Au+Au collisions at RHIC. Therefore it will be produced at LHC. Since sQGP is produced by deutronAu collisions at RHIC (in the forward direction), it will also be produced through p-p collisions at LHC. This begins a new era of physics.” Starting in 2007 the LHC will collide the pro√ ton beams at s=14 TeV and the lead beams at √ sNN =5.5 TeV, and the luminosity of these two colli-

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sion mode is 5×1030 and 5×1026 cm?2 ·s?1 respectively. The center of mass energy for collisions of the heaviest ions at the ALICE will exceed that available at BNL/RHIC by a factor of about 30[91] . Collisions at these previously un-explored energies o?er opportunities to create extreme conditions which are higher energy densities (in the regime ε ≈1—1000 GeV/fm3 ), larger volumes and longer timescales than in RHIC. ALICE is a general-purpose heavy ion experiment designed to study the physics of strongly interacting matter and the QGP in nucleus-nucleus collisions at the LHC[6] . The unique capabilities include its low transverse momentum (pT ) acceptance, excellent vertexing, particle identi?cation over a broad pT range and jet reconstruction[6, 92, 93] . 1) The dNch /dy could reach up to 2×103—8×103, which is the most fundamental observable to investigate properties of the medium created in the collisions. The charged particle rapidity density is ex√ pected to follow Feynman scaling with s, and the multiplicity distribution is expected to show strong departure from KNO scaling. All of these can be studied by ALICE. 2) ALICE experiment measures and identi?es particles over a wide pT range (from 100 MeV/c to 100 GeV/c). Studies on pT spectra are important

to understand any new physics at LHC energies. 3) ALICE can measure and identify photons over a large pT range with Photon Spectrometer (PHOS). Measurements of inclusive and direct photons are important signatures of QGP probing and initial information of the collisions. LHC is scheduled to deliver p-p beams at √ s=900 GeV late this year, possibly 14 TeV in 2008, and Pb+Pb beams at 5.5 TeV in 2008. The LHC/ALICE will certainly open up new aspects of physics for us. As analysis work for the RHIC’s ?rst three run and SPS data, physical scientists have been achieving many great results, and ?nding many signatures of QGP, phase transition and decon?nement of color. However, the research for these physical goals is just on the way. The RHIC and GSI are currently updating their detectors, and many accelerators are planning to be established in many countries. Absolutely, to us the most expecting experiment in the near future is LHC at CERN. We are looking forward to the exciting experimental data of the ?rst p-p collisions at 900 GeV from LHC/ALICE. It will help us to have a further and deeply understanding of the properties of the QGP state, QCD phase transition and chiralsymmetry restoration.

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